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A344809 Numbers that are the sum of six squares in five or more ways.

%I A344809 #11 May 10 2024 01:38:39
%S A344809 54,57,60,62,63,65,66,68,69,70,71,72,73,74,75,76,77,78,79,80,81,83,84,
%T A344809 85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,
%U A344809 106,107,108,109,110,111,112,113,114,115,116,117,118,119,120
%N A344809 Numbers that are the sum of six squares in five or more ways.
%H A344809 Sean A. Irvine, <a href="/A344809/b344809.txt">Table of n, a(n) for n = 1..1000</a>
%e A344809 57 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 7^2
%e A344809    = 1^2 + 1^2 + 1^2 + 2^2 + 5^2 + 5^2
%e A344809    = 1^2 + 1^2 + 1^2 + 3^2 + 3^2 + 6^2
%e A344809    = 1^2 + 2^2 + 2^2 + 4^2 + 4^2 + 4^2
%e A344809    = 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 5^2
%e A344809    = 2^2 + 2^2 + 2^2 + 2^2 + 4^2 + 5^2
%e A344809 so 57 is a term.
%o A344809 (Python)
%o A344809 from itertools import combinations_with_replacement as cwr
%o A344809 from collections import defaultdict
%o A344809 keep = defaultdict(lambda: 0)
%o A344809 power_terms = [x**2 for x in range(1, 1000)]
%o A344809 for pos in cwr(power_terms, 6):
%o A344809     tot = sum(pos)
%o A344809     keep[tot] += 1
%o A344809     rets = sorted([k for k, v in keep.items() if v >= 5])
%o A344809     for x in range(len(rets)):
%o A344809         print(rets[x])
%Y A344809 Cf. A344798, A344808, A344810, A345482, A345514.
%K A344809 nonn
%O A344809 1,1
%A A344809 _David Consiglio, Jr._, Jun 20 2021